| Label |
Polynomial |
Degree |
Signature |
Discriminant |
Ram. prime count |
Root discriminant |
Galois root discriminant |
CM field |
Galois |
Monogenic |
Galois group |
Class group |
Unit group torsion |
Unit group rank |
Regulator |
| 6.0.11691.1 |
$x^{6} - x^{5} - x^{2} + x + 1$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 433$ |
$2$ |
$4.76403865609$ |
$36.0416425818802$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$6$ |
$2$ |
$0.691359666578$ |
| 6.0.16551.1 |
$x^{6} - x^{5} - x^{4} + 3 x^{3} - 2 x + 1$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 613$ |
$2$ |
$5.04820953884$ |
$42.883563284783136$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$6$ |
$2$ |
$0.932873082902$ |
| 6.0.22592.1 |
$x^{6} - 2 x^{5} + 2 x^{4} - x^{2} + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 353$ |
$2$ |
$5.316907603$ |
$37.57658845611187$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$4$ |
$2$ |
$0.752120362427$ |
| 6.0.23031.1 |
$x^{6} + x^{4} - x^{3} + x^{2} - 2 x + 1$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 853$ |
$2$ |
$5.33398920661$ |
$50.586559479766954$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$6$ |
$2$ |
$1.18590232532$ |
| 6.0.24003.1 |
$x^{6} - x^{5} + 3 x^{3} - x^{2} - 2 x + 1$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 7\cdot 127$ |
$3$ |
$5.3708652218$ |
$51.64300533470143$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$6$ |
$2$ |
$1.15781781619$ |
| 6.2.30125.1 |
$x^{6} - x^{5} + x^{4} - 2 x^{2} + x - 1$ |
$6$ |
[2,2] |
$5^{3}\cdot 241$ |
$2$ |
$5.57811986838$ |
$34.713109915419565$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$3$ |
$0.50437245294$ |
| 6.0.31347.1 |
$x^{6} - 3 x^{4} - 2 x^{3} + 3 x^{2} + 3 x + 1$ |
$6$ |
[0,3] |
$-\,3^{6}\cdot 43$ |
$2$ |
$5.61520992871$ |
$24.357295210976567$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$6$ |
$2$ |
$1.57963516749$ |
| 6.0.34371.1 |
$x^{6} - x^{5} - 2 x^{3} + 2 x + 1$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 19\cdot 67$ |
$3$ |
$5.70206321806$ |
$61.7980582219215$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$6$ |
$2$ |
$1.68719062958$ |
| 6.2.35125.1 |
$x^{6} - x^{5} - x^{4} + 2 x^{3} - x^{2} + 1$ |
$6$ |
[2,2] |
$5^{3}\cdot 281$ |
$2$ |
$5.72272296207$ |
$37.48332962798263$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$3$ |
$0.563512855802$ |
| 6.0.40203.1 |
$x^{6} - x^{5} - 3 x^{4} + 4 x^{3} + 3 x^{2} - 4 x + 1$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 1489$ |
$2$ |
$5.85297151238$ |
$66.83561924602779$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$6$ |
$2$ |
$1.87209597052$ |
| 6.0.41823.1 |
$x^{6} - 2 x^{5} - 2 x^{4} + 5 x^{3} + x^{2} - 3 x + 1$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 1549$ |
$2$ |
$5.89163540923$ |
$68.16890786861705$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$6$ |
$2$ |
$1.78702959953$ |
| 6.0.44496.1 |
$x^{6} - x^{5} + x^{4} - 2 x^{3} + x^{2} + 3 x + 1$ |
$6$ |
[0,3] |
$-\,2^{4}\cdot 3^{3}\cdot 103$ |
$3$ |
$5.95278451666$ |
$49.71921157862421$ |
|
|
|
$C_3^2:D_4$ (as 6T13) |
trivial |
$6$ |
$2$ |
$2.0030873169$ |
| 6.0.47680.1 |
$x^{6} + x^{2} - 2 x + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 5\cdot 149$ |
$3$ |
$6.02174981256$ |
$54.589376255824725$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$4$ |
$2$ |
$1.27956995152$ |
| 6.0.47979.1 |
$x^{6} - 3 x^{5} + 2 x^{4} - x^{3} + x^{2} + 2 x + 1$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 1777$ |
$2$ |
$6.02802713568$ |
$73.01369734508724$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$6$ |
$2$ |
$2.10098751175$ |
| 6.0.49408.1 |
$x^{6} - x^{4} - 2 x^{3} + x^{2} + 2 x + 1$ |
$6$ |
[0,3] |
$-\,2^{8}\cdot 193$ |
$2$ |
$6.0575854024$ |
$35.006765233586634$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$4$ |
$2$ |
$1.8510118889$ |
| 6.2.49664.1 |
$x^{6} - 2 x^{5} + 3 x^{4} - 2 x^{3} - 1$ |
$6$ |
[2,2] |
$2^{9}\cdot 97$ |
$2$ |
$6.06280522016$ |
$27.85677655436824$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$3$ |
$0.724060154938$ |
| 6.0.50139.1 |
$x^{6} - x^{5} + 2 x^{4} - x^{3} - x^{2} + 2 x + 1$ |
$6$ |
[0,3] |
$-\,3^{4}\cdot 619$ |
$2$ |
$6.07243131636$ |
$56.713475908776786$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$6$ |
$2$ |
$2.5046218031$ |
| 6.2.51125.1 |
$x^{6} - 2 x^{5} + 2 x^{4} - 2 x^{2} + 3 x - 1$ |
$6$ |
[2,2] |
$5^{3}\cdot 409$ |
$2$ |
$6.09217289661$ |
$45.221676218380054$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$3$ |
$0.755100154139$ |
| 6.2.52625.1 |
$x^{6} - 2 x^{4} - x^{3} + x^{2} + x - 1$ |
$6$ |
[2,2] |
$5^{3}\cdot 421$ |
$2$ |
$6.12160568228$ |
$45.880278987817846$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$3$ |
$0.796637527934$ |
| 6.0.53568.1 |
$x^{6} - 2 x^{5} + 2 x^{4} + 2 x + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 3^{3}\cdot 31$ |
$3$ |
$6.13975307555$ |
$38.57460304397182$ |
|
|
|
$C_3^2:D_4$ (as 6T13) |
trivial |
$6$ |
$2$ |
$2.26310925611$ |
| 6.2.56125.1 |
$x^{6} - x^{5} + x^{3} - 3 x^{2} + 2 x - 1$ |
$6$ |
[2,2] |
$5^{3}\cdot 449$ |
$2$ |
$6.18765454266$ |
$47.38143096192854$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$3$ |
$0.807045361974$ |
| 6.0.57591.1 |
$x^{6} - 3 x^{4} - x^{3} + 3 x^{2} + 1$ |
$6$ |
[0,3] |
$-\,3^{6}\cdot 79$ |
$2$ |
$6.21430316634$ |
$33.014777723463894$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$6$ |
$2$ |
$2.57756117717$ |
| 6.0.59648.1 |
$x^{6} - 2 x^{5} + 2 x^{3} - 2 x^{2} + 2$ |
$6$ |
[0,3] |
$-\,2^{8}\cdot 233$ |
$2$ |
$6.25075745793$ |
$38.46372031452967$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$4$ |
$2$ |
$2.11015173442$ |
| 6.0.59967.1 |
$x^{6} - x^{5} - x^{4} + x^{3} + 4 x^{2} - 6 x + 3$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 2221$ |
$2$ |
$6.25631663506$ |
$81.62720134857007$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$6$ |
$2$ |
$2.61522574479$ |
| 6.0.60992.1 |
$x^{6} + 3 x^{4} - 2 x^{3} + 4 x^{2} - 2 x + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 953$ |
$2$ |
$6.27401393708$ |
$61.741396161732524$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$4$ |
$2$ |
$1.4085735579$ |
| 6.0.65600.1 |
$x^{6} - 2 x^{5} - x^{4} + 2 x^{3} + 2 x^{2} - 2 x + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 5^{2}\cdot 41$ |
$3$ |
$6.35063725183$ |
$37.44569770046876$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$4$ |
$2$ |
$1.57718616336$ |
| 6.0.70659.1 |
$x^{6} - x^{5} + 2 x^{4} - 2 x^{3} + 4 x^{2} + 3$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 2617$ |
$2$ |
$6.42975731391$ |
$88.60586888011426$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$6$ |
$2$ |
$2.68253508466$ |
| 6.2.71125.1 |
$x^{6} - 2 x^{5} - x^{4} + 3 x^{3} - x - 1$ |
$6$ |
[2,2] |
$5^{3}\cdot 569$ |
$2$ |
$6.43680540493$ |
$53.33854141237835$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$3$ |
$0.946078446571$ |
| 6.0.72716.1 |
$x^{6} - x^{5} - x^{3} + 2 x^{2} + 2 x + 1$ |
$6$ |
[0,3] |
$-\,2^{2}\cdot 7^{3}\cdot 53$ |
$3$ |
$6.4605823038$ |
$30.57550357757$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$2$ |
$1.1567540312$ |
| 6.0.73467.1 |
$x^{6} - x^{5} + 3 x^{4} - 4 x^{3} + 4 x^{2} - 3 x + 3$ |
$6$ |
[0,3] |
$-\,3^{4}\cdot 907$ |
$2$ |
$6.47165540349$ |
$68.65063908948638$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$6$ |
$2$ |
$3.28175755181$ |
| 6.2.82000.1 |
$x^{6} - x^{5} + 2 x^{4} - x^{3} + 2 x^{2} - 3 x + 1$ |
$6$ |
[2,2] |
$2^{4}\cdot 5^{3}\cdot 41$ |
$3$ |
$6.59126807661$ |
$22.728124217737328$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$3$ |
$1.08012171661$ |
| 6.0.82496.1 |
$x^{6} - 2 x^{4} - 2 x^{3} + 2 x^{2} + 2 x + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 1289$ |
$2$ |
$6.59789624667$ |
$71.80529228406496$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$4$ |
$2$ |
$2.71640848093$ |
| 6.2.82625.1 |
$x^{6} - x^{5} + x^{4} - 3 x^{3} + 2 x^{2} - 2 x + 1$ |
$6$ |
[2,2] |
$5^{3}\cdot 661$ |
$2$ |
$6.5996146625$ |
$57.48912940721924$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$3$ |
$1.0798068604$ |
| 6.0.82971.1 |
$x^{6} - x^{5} - 4 x^{4} + 4 x^{3} + 4 x^{2} - 6 x + 3$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 7\cdot 439$ |
$3$ |
$6.60421273124$ |
$96.01562372864116$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$6$ |
$2$ |
$3.03529324049$ |
| 6.0.85131.1 |
$x^{6} - x^{5} - 2 x^{4} + 3 x^{3} + 3 x^{2} - 6 x + 3$ |
$6$ |
[0,3] |
$-\,3^{4}\cdot 1051$ |
$2$ |
$6.63256155361$ |
$73.8996359684178$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$6$ |
$2$ |
$3.61598090647$ |
| 6.2.87625.1 |
$x^{6} - 2 x^{5} + 2 x^{4} + x^{3} - 3 x^{2} + x + 1$ |
$6$ |
[2,2] |
$5^{3}\cdot 701$ |
$2$ |
$6.66455779476$ |
$59.20304046246274$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$3$ |
$1.12777328898$ |
| 6.0.87831.1 |
$x^{6} - 3 x^{5} + 5 x^{4} - x^{3} - 2 x^{2} + 2 x + 1$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 3253$ |
$2$ |
$6.66716655559$ |
$98.78765105011861$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$6$ |
$2$ |
$3.41694141639$ |
| 6.0.91719.1 |
$x^{6} - x^{5} - x^{4} + x^{3} - 2 x^{2} + 3$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 43\cdot 79$ |
$3$ |
$6.71547214188$ |
$100.9504829111778$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$6$ |
$2$ |
$3.42713739389$ |
| 6.0.94311.1 |
$x^{6} - 2 x^{5} + 4 x^{4} - x^{3} + x^{2} + 3 x + 1$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 7\cdot 499$ |
$3$ |
$6.74673613105$ |
$102.36698686588367$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$6$ |
$2$ |
$2.96245072877$ |
| 6.0.95607.1 |
$x^{6} - x^{5} - x^{4} - 3 x^{3} + 6 x^{2} - 2 x + 1$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 3541$ |
$2$ |
$6.76210040788$ |
$103.06793875885944$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$6$ |
$2$ |
$2.8847228253$ |
| 6.0.96512.1 |
$x^{6} + x^{4} - 2 x^{3} - x^{2} + 2 x + 1$ |
$6$ |
[0,3] |
$-\,2^{8}\cdot 13\cdot 29$ |
$3$ |
$6.77272672685$ |
$48.92648348663579$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$4$ |
$2$ |
$2.88252286169$ |
| 6.0.96579.1 |
$x^{6} - x^{5} - x^{4} + 4 x^{3} - 2 x^{2} - 3 x + 3$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 7^{2}\cdot 73$ |
$3$ |
$6.77351012078$ |
$54.15277927484491$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$6$ |
$2$ |
$3.33201105544$ |
| 6.0.96832.1 |
$x^{6} - 2 x^{5} + 2 x^{4} - 2 x^{3} - x^{2} + 2 x + 1$ |
$6$ |
[0,3] |
$-\,2^{6}\cdot 17\cdot 89$ |
$3$ |
$6.77646423181$ |
$77.79460135510689$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$4$ |
$2$ |
$1.81789725839$ |
| 6.2.100125.1 |
$x^{6} - 2 x^{5} + 4 x^{4} - 4 x^{3} + 2 x^{2} + x - 1$ |
$6$ |
[2,2] |
$3^{2}\cdot 5^{3}\cdot 89$ |
$3$ |
$6.81433931037$ |
$36.53765181289022$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$3$ |
$1.12511265656$ |
| 6.2.102625.1 |
$x^{6} - 2 x^{5} + x^{4} + x^{3} - x^{2} - 1$ |
$6$ |
[2,2] |
$5^{3}\cdot 821$ |
$2$ |
$6.8424063441$ |
$64.07027391856539$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$3$ |
$1.24758735013$ |
| 6.0.103383.1 |
$x^{6} - x^{5} - 2 x^{4} + 4 x^{3} + x^{2} - 6 x + 4$ |
$6$ |
[0,3] |
$-\,3^{3}\cdot 7\cdot 547$ |
$3$ |
$6.85080367069$ |
$107.17742299570372$ |
|
|
? |
$C_3^2:D_4$ (as 6T13) |
trivial |
$6$ |
$2$ |
$3.22536551708$ |
| 6.2.103625.1 |
$x^{6} - x^{5} + x^{4} + x^{3} + 2 x + 1$ |
$6$ |
[2,2] |
$5^{3}\cdot 829$ |
$2$ |
$6.85347380632$ |
$64.38167441127949$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$3$ |
$1.31410369037$ |
| 6.0.104112.1 |
$x^{6} - x^{5} - 2 x^{4} + 5 x^{3} + 2 x^{2} - 3 x + 1$ |
$6$ |
[0,3] |
$-\,2^{4}\cdot 3^{3}\cdot 241$ |
$3$ |
$6.85883146573$ |
$42.68308608978487$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$6$ |
$2$ |
$3.81196345016$ |
| 6.0.104571.1 |
$x^{6} - x^{5} + 2 x^{3} + x^{2} - 3 x + 3$ |
$6$ |
[0,3] |
$-\,3^{4}\cdot 1291$ |
$2$ |
$6.86386200342$ |
$81.90380197349975$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$6$ |
$2$ |
$4.22934423242$ |
| 6.4.104875.1 |
$x^{6} - 2 x^{5} - x^{4} + x^{3} + 2 x^{2} + x - 1$ |
$6$ |
[4,1] |
$-\,5^{3}\cdot 839$ |
$2$ |
$6.86718365572$ |
$64.7688196588451$ |
|
|
✓ |
$C_3^2:D_4$ (as 6T13) |
trivial |
$2$ |
$4$ |
$1.37486382678$ |
